High Dynamic Range Tranceiver for Cognitive Radio

ABSTRACT

Embodiments of cognitive radio technology can recover and utilize underutilized portions of statically-allocated radio-frequency spectrum. A plurality of sensing methods can be employed. Transmission power control can be responsive to adjacent channel measurements. Digital pre-distortion techniques can enhance performance. Embodiments of a high DNR transceiver architecture can be employed.

PRIORITY

This application is related to and claims priority under 35 U.S.C.119(e) to U.S. Provisional Patent Application No. 60/890,801 filed onFeb. 20, 2007 entitled “SYSTEM AND METHOD FOR COGNITIVE RADIO” by HaiyunTang the complete content of which is hereby incorporated by reference.

BACKGROUND

1. Field of the Invention

The inventions herein described relate to systems and methods forcognitive radio.

2. Description of the Related Art

Spectrum Utilization Problems

A recent study by the FCC Spectrum Task Force [United States' FederalCommunications Commission (FCC), “Report of the spectrum efficiencyworking group,” November 2002,http://www.fcc.gov/sptf/files/IPWGFinalReport.pdf] found that while theavailable spectrum becomes increasingly scarce, the assigned spectrum issignificantly underutilized. This imbalance between spectrum scarcityand spectrum underutilization is especially inappropriate in thisInformation Age, when a significant amount of spectrum is needed toprovide ubiquitous wireless broadband connectivity, which isincreasingly becoming an indispensable part of everyday life.

Static spectrum allocation over time can also result in spectrumfragmentation. With lack of an overall plan, spectrum allocations in theUS and other countries over the past several decades can appear to berandom.

Despite some efforts to serve best interests at the time, this leads tosignificant spectrum fragmentation over time. The problem is exacerbatedat a global level due to a lack of coordinated regional spectrumassignments. In order to operate under such spectrum conditions, adevice can benefit from operational flexibility in frequency and/or bandshape; such properties can help to maximally exploit local spectrumavailability.

To address the above problems, an improved radio technology is neededthat is capable of dynamically sensing and locating unused spectrumsegments, and, communicating using these spectrum segments whileessentially not causing harmful interference to designated users of thespectrum. Such a radio is generally referred to as a cognitive radio,although strictly speaking, it may perform only spectrum cognitionfunctions and therefore can be a subtype of a broad-sense cognitiveradio [J. M. III, “Cognitive radio for flexible mobile multimediacommunications,” Mobile Networks and Applications, vol. 6, September2001.] that learns and reacts to its operating environment. Key aspectsof a cognitive radio can include:

-   Sensing: a capability to identify used and/or unused segments of    spectrum.-   Flexibility: a capability to change operating frequency and/or band    shape; this can be employed to fit into unused spectrum segments.

Non-interference: a capability to avoid causing harmful interference todesignated users of the spectrum.

Such a cognitive radio technology can improve spectrum efficiency bydynamically exploiting underutilized spectrum, and, can operate at anygeographic region without prior knowledge about local spectrumassignments. It has been an active research area recently.

FCC Spectrum Reform Initiatives

FCC has been at the forefront of promoting new spectrum sharingtechnologies. In April 2002, the FCC issued an amendment to Part 15rules that allows ultra-wideband (UWB) underlay in the existing spectrum[FCC, “FCC first report and order: Revision of part 15 of thecommission's rules regarding ultra-wideband transmission systems,” ETDocket No. 98-153, April 2002]. In June 2002, the FCC established aSpectrum Policy Task Force (SPTF) whose study on the current spectrumusage concluded that “many portions of the radio spectrum are not in usefor significant periods of time, and that spectrum use of these ‘whitespaces’ (both temporal and geographic) can be increased significantly”.SPTF recommended policy changes to facilitate “opportunistic or dynamicuse of existing bands.” In December 2003, FCC issued the notice ofproposed rule making on “Facilitating Opportunities for Flexible,Efficient and Reliable Spectrum Use Employing Cognitive RadioTechnologies” [FCC, “Facilitating opportunities for flexible, efficient,and reliable spectrum use employing cognitive radio technologies,” ETDocket No. 03-108, December 2003] stating that “by initiating thisproceeding, we recognize the importance of new cognitive radiotechnologies, which are likely to become more prevalent over the nextfew years and which hold tremendous promise in helping to facilitatemore effective and efficient access to spectrum.”

While both UWB and cognitive radio are considered as spectrum sharingtechnologies, their approaches to spectrum sharing are substantiallydifferent. UWB is an underlay (below noise floor) spectrum sharingtechnology, while cognitive radio is an overlay (above noise floor) andinterlay (between primary user signals) spectrum sharing technology asshown in FIG. 1. Through sensing combined with operational flexibility,a cognitive radio can identify and make use of spectral “white spaces”between primary user signals. Because a cognitive user signal resides insuch “white spaces”, high signal transmission power can be permitted aslong as signal power leakage into primary user bands does not embodyharmful interference.

Broadcast TV Bands.

Exemplary broadcast TV bands are shown in Graph 200 of FIG. 2. Each TVchannel is 6 MHz wide. Between 0 and 800 MHz, there are a total of 67 TVchannels (Channels 2 to 69 excluding Channel 37 which is reserved forradio astronomy). The NPRM [FCC, May 2004, op. cit.] excludes certainchannels for unlicensed use: Channels 2-4, which are used by TVperipheral devices, and Channels 52-69, which are considered for futureauction. Among the channels remaining, Channels 5-6, 7-13, 21-36, and38-51 are available for unlicensed use in all areas. Unlicensed use inChannels 14-20 is allowed only in areas where they are not used bypublic safety agencies [FCC, May 2004, op. cit.].

It can be appreciated that Channels 52-69 are currently used by TVbroadcasters and it is not clear if/when they will be vacated. There issignificant interference in the lower channels 5-6 and 7-13. Based onthese considerations, the spectrum segment 470-806 MHz covering TVchannels 14-69 can be of particular interest.

Spectrum Opportunity in the TV Bands

Spectrum opportunity can be a direct result of incumbent systeminefficiency. In TV bands, a signal from a TV tower can cover an areawith a radius of tens of kilometers. TV receivers can be sensitive tointerference such that TV cell planning may be very conservative toensure there is essentially no co-channel interference. This can leave asubstantial amount of “white spaces” between co-channel TV cells asillustrated in the the Map 300 of FIG. 3. Those “white spaces” canconstitute an opportunistic region for cognitive users on a particularTV channel. Each TV channel may have a differently shaped opportunisticregion. The total spectrum opportunity at any location can comprise thetotal number of opportunistic regions covering the location. Ameasurement in one locality shows an average spectrum opportunity in TVchannels 14-69 of about 28 channels; that can be expressed as anequivalent bandwidth of approximately 170 MHz.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 graph of spectrum sharing technologies: UWB and cognitive radio

FIG. 2 graph of exemplary television channel bands

FIG. 3 map of television co-channel coverage areas and opportunisticregion

FIG. 4 diagram: cognitive radio system

FIG. 5 diagram: amplification stages between antenna and ADC

FIG. 6 diagram: heterodyne receiver

FIG. 7 diagram: heterodyne transceiver

FIG. 8 diagram: wideband direct-conversion receiver

FIG. 9 graph: frequency-domain non-linear effect

FIG. 10 diagram: double-ADC receiver architecture

FIG. 11 diagram: double-ADC receiver architecture, detail

FIG. 12 graph: image problem, image rejection filter

FIG. 13 graph: solution for LO freq. with specified IF freq. 140 MHz

FIG. 14 graph: solution for LO freq. with specified IF freq. 70 MHz

FIG. 15 graph: solution for LO freq. with specified IF freq. 140 MHz andspecified rejection margin

FIG. 16 graph: example SAW filter response

FIG. 17 graph: example SAW filter rejection mask

FIG. 18 graph: RF gain requirements

FIG. 19 diagram: heterodyne receiver, single-channel

FIG. 20 diagram: wideband direct-conversion transmitter

FIG. 21 graph: DTV transmission mask

FIG. 22 Diagram: wideband direct-conversion transmitter, detail

FIG. 23 graph: simulated signal spectra for specified devicenon-linearities.

DETAILED DESCRIPTION

FIG. 4 depicts an embodiment of a cognitive radio system in blockdiagram. A transceiver 401 can be coupled with and/or in communicationwith one or more antennae 402. Baseband signal processing can beprovided by elements of a baseband processor 403. Elements of a basebandprocessor 403 can comprise a sensing processor 404, a transmit powercontrol element 405, and a pre-distortion element 406. In someembodiments a pre-distortion element 406 can be coupled with and/or incommunication with a transceiver 401. In some embodiments a transmitpower control element can be coupled with and/or in communication with atransceiver 401. In some embodiments a collective sensing element 407can be coupled with and/or in communication with a baseband processor403 and/or elements comprising a baseband processor.

In some embodiments transceiver 401 can comprise transceiver and/ortransmitter and/or receiver mechanisms disclosed herein. In someembodiments sensing element 404 can comprise one or more sensingmechanisms as described herein. By way of example and not limitationthese sensing mechanisms can include energy sensing, NTSC signalsensing, and/or ATSC signal sensing. In some embodiments a collectivesensing element 407 can provide collective sensing mechanisms asdescribed herein.

In some embodiments transmit power control 405 can support adaptivetransmit power control mechanisms described herein. In some embodimentspre-distortion element 406 can provide digital pre-distortion mechanismsas described herein.

In some embodiments baseband processor 403 can support additionalprocessing mechanisms as described herein. By way of example and notlimitation these mechanisms can include filtering and/or reconstruction.

RF System Analysis Input Signal Dynamic Range

The diagram 200 of FIG. 2 depicts an embodiment of a channel-basedsignal transmission scheme. Each of the channel signals in an embodimentcan be considered to be independent. Hence, the total signal power overall channels considered (for example, TV Channels 14-69) can be computedas the sum of the individual signal powers of those channels.

Considering the wideband signal over all the channels in an embodimentcomprising TV channels, a total signal bandwidth can be 336 MHz and anantenna thermal noise floor over the signal bandwidth can be calculated:

$\begin{matrix}\begin{matrix}{N_{0}^{dB} = {10\; {\log_{10}({kTB})}}} \\{= {{- 174} + {10\; {\log_{10}\left( {336 \times 10^{6}} \right)}}}} \\{\approx {{- 89}\mspace{14mu} {dBm}}}\end{matrix} & (1)\end{matrix}$

In some embodiments, a maximum measured signal power can beapproximately −20 dBm.

For an individual TV channel in an embodiment, a thermal noise floor canbe

n ₀ ^(dB)=−174+10 log₁₀(6×10⁶)≈106 dBm   (2)

In some embodiments, a maximum single-channel power can have a value ofapproximately −20 dBm. In an embodiment of a cognitive radio system thatoperates close to the noise floor, a receiver can see a channel powerdisparity of

−20−(−106+6)≈80 dB   (3)

assuming a receiver noise figure of 6 dB.

Third-Order Intermodulation

In an ideal RF receive chain, all RF components can be perfectly linearand there is no distortion on the received signal after the signal hasbeen processed by the RF receive chain. Real-world RFcomponents—especially active RF components like amplifiers andmixers—can exhibit some degree of nonlinearity, resulting in signaldistortion. Small-signal nonlinearity of a single RF component orcascaded RF components can be modeled by the following input-outputrelationship

y(t)=α₀+α₁ x(t)+α₂ x ²(t)+α₃ x ³(t)+  (4)

where x(t) is the input signal and y(t) is the output signal and in sometypical embodiments the nonlinearity can be dominated by the low-ordernonlinear terms.

RF components typically operate on passband signals. For passbandsignals, even-order nonlinear terms can be discarded when appropriatefiltering is performed on the RF chain. The small signal nonlinearitycan then be approximated as:

y(t)≈α₁x(t)+α₃x(t)   (5)

retaining only the lowest odd order distortion term.

When a passband signal with baseband equivalent representation s_(B)(t)passes through an element with nonlinear transfer function (3), thebaseband equivalent representation of the output signal can be expressedas

$\begin{matrix}{\underset{\underset{Signal}{}}{\alpha_{1}{s_{B}(t)}} + \underset{\underset{3{rd}\text{-}{order}\mspace{14mu} {distortion}}{}}{\frac{3\alpha_{3}}{4}{{s_{B}(t)}}^{2}{s_{B}(t)}}} & (6)\end{matrix}$

At the output, the ratio of the distortion power to the signal power,which is also the inverse of the dynamic range, can be expressed as:

$\begin{matrix}{\begin{matrix}{P_{DR}^{- 1} = \frac{\left( \frac{3\alpha_{3}}{4} \right)^{2}{E\left\lbrack {{s_{B}(t)}}^{6} \right\rbrack}}{\alpha_{1}^{2}{E\left\lbrack {{s_{B}(t)}}^{2} \right\rbrack}}} \\{= \frac{\left( \frac{3\alpha_{3}}{4} \right)^{2}{E\left\lbrack {{s_{B}(t)}}^{6} \right\rbrack}}{\alpha_{1}^{2}{E\left\lbrack {{s_{B}(t)}}^{2} \right\rbrack}}} \\{= {\frac{1}{\alpha_{1}^{2}}\left( \frac{3\alpha_{3}}{4} \right)^{2}\left\{ {E\left\lbrack {{s_{B}(t)}}^{2} \right\rbrack} \right\}^{2}\Gamma}}\end{matrix}{where}} & (7) \\{\Gamma = \frac{E\left\lbrack {{s_{B}(t)}}^{6} \right\rbrack}{\left\{ {E\left\lbrack {{s_{B}(t)}}^{2} \right\rbrack} \right\}^{3}}} & (8)\end{matrix}$

is a factor that depends essentially only on the signal structure ofs_(B)(t). For example, Γ is approximately 7.5 dB if s_(B)(t) is whitenoise. Suppose s_(B)(t) is a combined signal over all TV channels withpower

P _(In) =E[|s _(B)(t)|²]  (9)

The gain can be defined

g=α₁ ²   (10)

and output signal power

P_(Signal)=gP_(In)   (11)

Using a two-tone IP3 relationship

$\begin{matrix}{{\frac{1}{\alpha_{1}^{2}}\left( \frac{3\alpha_{3}}{4} \right)^{2}} = \frac{g^{2}}{P_{{IP}\; 3}^{2}}} & (12)\end{matrix}$

It can be appreciated that a third-order intercept point (IP3 or TOI) isthe point at which a linear extrapolation (as a function of input power)of linear output power and third-order distortion power level meet.

Thus

$\begin{matrix}{P_{DR}^{- 1} = {{\frac{g^{2}}{P_{{IP}\; 3}^{2}}P_{In}^{2}\Gamma} = {\frac{P_{Signal}^{2}}{P_{{IP}\; 3}^{2}}\Gamma}}} & (13)\end{matrix}$

or in dB scale

$\begin{matrix}{P_{DR}^{dB} = {{2P_{{IP}\; 3}^{dB}} - {2P_{Signal}^{dB}} - \Gamma^{dB}}} & (14)\end{matrix}$

Since the output 3rd-order distortion power is

$\begin{matrix}{P_{{IM}\; 3} = {\left( \frac{3\alpha_{3}}{4} \right)^{2}{E\left\lbrack {{s_{B}(t)}}^{6} \right\rbrack}}} & (15)\end{matrix}$

then, according to Equations (7) and (14)

$\begin{matrix}\begin{matrix}{P_{{IM}\; 3}^{dB} = {P_{Signal}^{dB} - P_{DR}^{dB}}} \\{= {{3P_{Signal}^{dB}} - {2P_{{IP}\; 3}^{dB}} + \Gamma^{dB}}}\end{matrix} & (16)\end{matrix}$

Note that the term Γ in Equation (16) accounts for added distortion thatcan result from a particular signal structure. When an input signals_(B)(t) is essentially a sinusoid (i.e. a single tone in frequencydomain), Γ^(dB)=0.

Overview of RF Receiver Functions

The functions of a RF receiver system can comprise: a) Frequencytranslation and channel selection; and b) Signal amplification.

Direct RF Sampling

An RF signal can reside in a particular frequency band

[f_(c)−W,f_(c)+W]

where f_(c) is a carrier frequency and 2 W is a signal bandwidth. Inorder to retrieve information content from the signal, the signal can bedigitized.

In theory, it is possible to directly sample the RF signal at a carrierfrequency. Such an approach, however, can be prohibitively expensive interms of hardware cost and power consumption. For example, if a carrierfrequency is 600 MHz, direct Nyquist sampling of an associated RF signalcan require a sampling frequency at least 2(f_(c)+W) or 1.2 GHz. In someembodiments an overall RF signal can contain both strong and weak signalcontents, e.g. both TV signals and cognitive radio signals. Ahigh-resolution ADC can be advantageously specified for some suchembodiments. By way of non-limiting example, for a power differencebetween the strong and weak signals of 70 dB, an ADC with a resolutionof at least 12 bits can be specified in some typical embodiments. SuchADC requirements can present realization challenges, given that someembodiments of current commercial ADCs can run at about 1 GHz samplingfrequency, with 8-bit resolution [National Semiconductor Corporation,“ADC081000 High Performance, Low Power 8-bit, 1 GSPS A/D Converter”,DS200681, 2004], [Maxim Integrated Products, “MAX108 Data Sheet: ±5V,1.5 Gsps, 8-Bit ADC with On-Chip 2.2 GHz Track/Hold Amplifier”, 19-1492;Rev 1; 10/01]. Direct RF sampling embodiments may become a increasinglyadvantageous in the future, as ADC and related technologies evolve.

Frequency Translation and Channel Selection

The high cost of RF direct sampling can be a result of the sampling ofunnecessary signal contents below f_(c)−W. Given an informationbandwidth of 2 W, Nyquist sampling only requires a sampling frequency of2 W in the circumstance that the signal center frequency can be shiftedfrom the carrier frequency f_(c) to DC, i.e.

[f_(c)−W,f_(c)+W]→[−W,W]  (17)

Such frequency translation can typically be achieved in an RF receiverthrough mixing. In addition to performing frequency translation, areceiver can also perform channel selection in order to acquire a signalin the desired 2 W-wide information band.

Signal Amplification

Another major function of an RF receiver can be signal amplification.Consider an 8-bit ADC receiving an input signal with peak-to-peakvoltage of 600 mV [Nat'l Semi. Corp., DS200681, 2004, op. cit.]. Anassociated quantization step can be 2.34 mV. The quantization noisepower assuming a 50-Ohm load can be expressed

$\begin{matrix}{N_{q}^{dB} = {{10\mspace{11mu} {\log_{10}\left\lbrack {2 \times \frac{\left( {2.34 \times 10^{- 3}} \right)^{2}}{12}\frac{10^{3}}{50}} \right\rbrack}} \approx {{- 47}\mspace{11mu} {dBm}}}} & (18)\end{matrix}$

where a factor of 2 results from considering the total quantizationnoise power of the in-phase (I) and quadrature (Q) ADCs in the system.

In some embodiments a received signal power level at the antenna can besmall, e.g. close to the exemplary thermal noise level of −89 dBm inEquation (1). As illustrated in diagram 500 (FIG. 5), significantamplification through multiple amplification stages along the RF chaincan be provided in some embodiments to ensure that a signal has enoughpower to overcome a quantization noise floor when the signal reaches anADC input. In some embodiments, a specification can be employed toensure that quantization noise has a negligible impact on the systemperformance; require that at the ADC input, the total thermal noise(amplified thermal noise plus RF chain noise figure) is at least X^(dB)(e.g. 10 dB) above the quantization noise level. This specification cantranslate into a requirement on the total RF chain power gain g_(RF):

g _(RF) ^(dB)−89 dBm+F _(RF) ^(dB)≧−47 dBm+X ^(dB)   (19)

where F_(RF) is the RF chain noise figure. Alternatively, thisrelationship can be expressed

g _(RF) ^(dB)≧42−F _(RF) ^(dB) +X ^(dB)   (20)

As an example, consider a receiver with a noise figure of 6 dB andX^(dB)=10 dB. The total gain provided by the RF chain needs to be atleast 46 dB according to the above equation. Accomplishing this gain canbe a non-trivial task.

Receiver Architecture Choices Based on Channel Selection Considerations

Since each exemplary 6 MHz TV channel can carry dissimilar informationcontent, in some embodiments channel selection can be employed to decodethe information content of a particular channel, such as a TV channel.Channel selection can be performed at one or more of an RF stage, IFstage, analog baseband, digital baseband, and/or a combination of thesestages.

RF Channel Selection:

In one design scenario, a channel selection filter can be disposed inthe RF stage immediately following the antenna in order to select thedesired channel. Several problems can attend this approach. First, ahigh quality channel selection filter can present challenges torealization at specified RF frequencies. A quality metric for a filtercan be defined as approximately its 3-dB bandwidth divided by its centerfrequency. For a specified fixed channel width, a corresponding qualitymetric value increases with increasing frequency. Hence, challenges torealizing such a filter can increase with frequency. In some embodimentsa receiver can be specified to select any one of 55 TV channels from anexemplary TV band. Thus in some embodiments, a tunable RF channelselection filter can be employed, thereby further exacerbatingrealization challenges. In some application embodiments, a capability ofsimultaneous decoding multiple (eg., TV) channels can be specified. Insome such embodiments a complete RF chain after a RF channel selectionfilter could be replicated for each additional channel, and can therebyincrease cost and/or complexity of a realizable embodiment.

Heterodyne Receiver:

Diagram 600 depicts a block diagram embodiment of a heterodyne receiver.

Channel selection in some embodiments of a conventional heterodynereceiver can be achieved through a combination of filtering stages alonga RF (radio frequency) chain, which are herein described:

An RF filter 604, also called a band selection filter. In someembodiments this can be an RF frequency filter connected directly toand/or coupled with an antenna 602. An RF filter 604 can select afrequency band of interest, such as an entire exemplary TV band, and canreject signals outside the frequency band of interest, e.g. 900 MHzcellular signals.

An Image rejection (IR) filter 612. In some embodiments this filter canbe disposed prior to a RF mixer 614 in order to reject one or more imagesignals. In some embodiments an image signal can otherwise fold into adesired signal band after mixing [B. Razavi, RF Microelectronics.Pearson-Prentice Hall, 1998].

An IF filter 616, also called a channel selection filter. In someembodiments this filter can be primarily responsible for channelselection. In some embodiments an IF filter 616 can be realized as astandalone component, e.g. a surface acoustic wave (SAW) filter [C.Marshall and et al., “2.7v GSM transceiver ICs with on-chip filtering,”ISSCC Digest of Technical Papers, pp. 148-149, February 1995].

One or more baseband filters 624 634, also called anti-aliasing filters.A baseband filter can be disposed prior to an analog to digitalconverter (ADC) in order to reject alias signals that can result fromsampling. Diagram 600 depicts baseband filter 624 employed incombination with ADC 628, and baseband filter 634 employed incombination with ADC 638, corresponding respectively to I and Q signalpaths of a receiver embodiment.

In some embodiments, with the exception of a band selection (RF) filter604, each of the filters just described can provide a degree of channelselection. In some embodiments a channel selection (IF) filter 616 canbe capable of providing the largest contribution to selectivity. In someembodiments a heterodyne receiver architecture can be relatively complexand/or costly if multiple channels are to be decoded simultaneously. Insome embodiments, an RF chain comprising the elements after the IRfilter can be replicated for each additional channel in order to supportsimultaneous decoding of multiple channels.

RF filter 604 can receive a signal from antenna 602. RF filter 604 canprovide a filtering function to a received signal. Low noise amplifierLNA 610 can be coupled with and receive a filtered signal from RF filter601.

LNA 610 can provide a gain function with low noise to a received signal.IR filter 612 can be coupled with and receive a gain-modified signalfrom LNA 610. IR filter 612 can provide a filtering function to areceived signal. Oscillator LO₁ 608 can provide a signal that can be atone signal at a specified frequency. RF mixer 614 can be coupled withand receive a filtered signal from IR filter 612. RF mixer 614 can becoupled with and receive a signal that can be a tone signal at aspecified frequency from oscillator LO₁ 608. RF mixer 614 can provide amixing function, providing a signal responsive to a combination of asignal received from IR filter 612 and a signal received from oscillatorLO₁ 608. IF filter 616 can be coupled with and receive a signal from RFmixer 614. IF filter 616 can provide a filtering function to a receivedsignal. IF amp 618 can be coupled with and receive a filtered signalfrom IF filter 616. IF amp 618 can provide a gain function to a receivedsignal.

Oscillator LO₂ 609 can provide a signal that can be a tone signal at aspecified frequency. Quad splitter 623 can provide a quadraturesplitting function to a received signal, thereby providing an in-phase(I) and a quadrature (Q) signal. Quad splitter 623 can be coupled withand receive a signal from Oscillator LO₂ 609. IF mixer 622 can becoupled with and receive a signal of a first specified phase from Quadsplitter 623. IF mixer 622 can be coupled with and receive again-modified signal from IF amp 618. IF mixer 622 can provide a mixingfunction, providing a signal responsive to a signal received from Quadsplitter 623 and responsive to a signal received from IF amp 618.Similarly, IF mixer 632 can provide a mixing function, providing asignal responsive to a signal of a second specified phase received fromQuad splitter 623 and responsive to a signal received from IF amp 618.Each of the baseband filters 624 634 can provide a filtering function toa corresponding received signal. Baseband filter 624 can be coupled withand receive a signal from IF mixer 622. Baseband filter 634 can becoupled with and receive a signal from IF mixer 632. Each of thevariable gain amplifiers (VGA) 626 636 can provide a variable gain to acorresponding received signal. VGA 626 can be coupled with and receive afiltered signal from baseband filter 624. VGA 636 can be coupled withand receive a filtered signal from baseband filter 634.

Each of the analog to digital converters (ADC) 628 628 can provide ananalog to digital conversion function to a corresponding received analogsignal. ADC 628 can be coupled with and receive a gain-modified signalfrom VGA 626. ADC 638 can be coupled with and receive a gain-modifiedsignal from VGA 636. ADC 628 can provide a baseband digital outputsignal corresponding to the first specified phase (I). ADC 638 canprovide a baseband digital output signal corresponding to the secondspecified phase (Q).

It can be appreciated that in alternative embodiments of a heterodynereceiver 600 and in other receiver and transmitter embodiments hereindescribed, various gain elements can be omitted and/or their functionsrealized by any known and/or convenient method of providing signal gain.

Heterodyne Transceiver:

Diagram 700 depicts a block diagram embodiment of a heterodynetransceiver. An upper portion of diagram 700 corresponds directly to theheterodyne receiver 600 discussed herein. It can be appreciated thatupon coupling antenna 702 to the receiver architecture through switch706, there can be essentially a one-to-one correspondence betweenelements of the receiver 600 and elements of the receiver portion of thetransceiver diagram 700.

The signal chain and function of the elements therein corresponddirectly and respectively between [Antenna 602, RF filter 604, LO₁ 608,LO₂ 609, LNA 610, IR filter 612, RF mixer 614, IF filter 616, IF amp618, IF mixer 622, Quad splitter 623, Baseband filter 624, VGA 626, ADC628, IF mixer 632, Baseband filter 634, VGA 636, ADC 638] and [Antenna702, RF filter 704, LO₁ 708, LO₂ 709, LNA 710, IR filter 712, RF mixer714, IF filter 716, IF amp 718, IF mixer 722, Quad splitter 723,Baseband filter 724, VGA 726, ADC 728, IF mixer 732, Baseband filter734, VGA 736, ADC 738].

The receiver portion of diagram 700 further comprises a Splitter 720that couples elements with each other: IF amp 718, IF mixer 722, and IFmixer 732. Corresponding elements IF amp 618, IF mixer 622, and IF mixer632 can be similarly coupled in the embodiment of diagram 600.

In some embodiments the transmitter portion of diagram 700 can beadvantageously realized using design analysis and/or frequencies and/orelement specifications and/or particular elements in common with thereceiver portion. In some embodiments elements RF filter 704, LO₁ 708,and LO₂ 709 can be used in common.

In some embodiments, elements of the transmitter [IR filter 712, RFmixer 714, IF filter 716, IF amp 718, Splitter 720, IF mixer 722, Quadsplitter 723, Baseband filter 724, VGA 726, IF mixer 732, Basebandfilter 734, VGA 736] can be substantially similar to the correspondingand respective elements of the receiver [IR filter 762, RF mixer 764, IFfilter 766, IF amp 768, Splitter 770, IF mixer 772, Quad splitter 773,Baseband filter 774, VGA 776, IF mixer 782, Baseband filter 784, VGA786].

Each of the digital to analog converters DAC 778 788 can provide adigital to analog conversion function to a corresponding receiveddigital signal, thereby providing corresponding converted correspondinganalog signals. Baseband filters 774 784 can each provide a filterfunction to a corresponding received signal. Baseband filter 774 can becoupled with and receive an analog signal from DAC 778. Baseband filter784 can be coupled with and receive an analog signal form DAC 788.

Oscillator LO₂ 709 can provide a signal that can be a tone signal at aspecified frequency. Quad splitter 773 can provide a quadraturesplitting function to a received signal, thereby providing an in-phase(I) and a quadrature (Q) signal. Quad splitter 773 can be coupled withand receive a signal from Oscillator LO₂ 709. IF mixer 772 can becoupled with and receive a signal of a first specified phase from Quadsplitter 773. IF mixer 772 can be coupled with and receive a filteredsignal from baseband filter 774. IF mixer 772 can provide a mixingfunction, providing a signal responsive to a signal received from Quadsplitter 773 and responsive to a signal received from Baseband filter774. Similarly, IF mixer 782 can provide a mixing function, providing asignal responsive to a signal of a second specified phase received fromQuad splitter 773 and responsive to a signal received from Basebandfilter 784.

Combiner 770 can provide a combining function, providing a signalresponsive to the combination of two received signals. Combiner 770 canbe coupled with and receive a signal corresponding to a first specifiedphase from IF mixer 772. Combiner 770 can be coupled with and receive asignal corresponding to a second specified phase from IF mixer 782. IFamp 778 can provide a gain function to a received signal. IF amp can becoupled with and receive a combined signal from Combiner 770. IF filtercan provide a filter function to a received signal. IF filter can becoupled with and receive a gain-modified signal from IF amp 778.

LO₁ 708 can provide a signal that can be a tone signal at a specifiedfrequency. RF mixer 764 can be coupled with and receive a filteredsignal from IF filter 766. RF mixer 764 can be coupled with and receivea signal that can be a tone signal at a specified frequency from LO₁708. RF mixer 764 can provide a mixing function, providing a signalresponsive to a combination of a signal received from IF filter 766 anda signal received from LO₁ 708. IR filter 762 can provide a filterfunction to a received signal. IR filter 762 can be coupled with andreceive a mixed signal from RF mixer 764. PA 760 can provide a poweramplification function to a received signal. PA 760 can be coupled withand receive a filtered signal from IR filter 762. RF filter 704 canprovide a filter function to a received signal. RF filter can be coupledwith and receive a signal from PA 760 via Switch 706. Switch 706 canselectably couple PA 760 with RF filter 704. Antenna 702 can provide anantenna transmission function to a power amplified signal received fromPA 760.

Wideband Direct-Conversion Receiver:

From the above discussion, it can be appreciated that as long as thechannel selection starts from a particular RF stage, in some embodimentsthe RF chain from that stage onward can be replicated for eachadditional channel. In some embodiments it can be advantageous to deferchannel selection all the way until the digital baseband. Such anembodiment can comprise a receiver that is capable of simultaneouslydecoding all of the channels in one or more specified bands, such as allof the TV channels in depicted in the graph 200. Two issues can beaddressed in such a system.

First, there can be a need to have fast and high-resolution sampling,because an ADC in such an embodiment sees an entire band of interest,such as a TV band (Channels 14-69) with 336 MHz of bandwidth.

Second, because before channel selection, the overall signal consists ofthe signals from all the channels, some of which can be strong whilesome of which can be weak, RF component nonlinearities can cause signalintermodulations between one or more channels and thus degrade systemperformance for the weak channels. Linearity requirements on RFcomponents constituting embodiments of such an architecture can thus berelatively stringent, especially on components disposed near to the ADCbecause such components can be specified to operate on relatively highpower signals and/or amplified input signals.

Current technology trends of digital scaling along with advances inhigh-speed ADCs can favor such an approach. An RF system design forembodiments of such a wideband direct-conversion receiver is hereindescribed; diagram 800 depicts an embodiment. Such an architecture maybe considered wideband because the RF receiver can operate on an entireband of interest, such as an entire TV band of 336 MHz bandwidth. Insome embodiments, a system comprises a direct-conversion architecturewherein an RF signal can be directly down-converted to a baseband.

RF filter 804 can receive a signal from antenna 802. RF filter 804 canprovide a filtering function to a received signal. Low noise amplifierLNA 806 can be coupled with and receive a filtered signal from RF filter804. LNA 806 can provide a gain function with low noise to a receivedsignal.

Oscillator LO 810 can provide a signal that can be a tone signal at aspecified frequency. Quad splitter 808 can provide a quadraturesplitting function to a received signal, thereby providing an in-phase(I) and a quadrature (Q) signal. Quad splitter 808 can be coupled withand receive a signal from LO 810. Mixer 820 can be coupled with andreceive a signal of a first specified phase from Quad splitter 808.Mixer 820 can be coupled with and receive a gain-modified signal fromLNA 806 . Mixer 820 can provide a mixing function, providing a signalresponsive to a signal received from Quad splitter 808 and responsive toa signal received from LNA 806. Similarly, Mixer 830 can provide amixing function, providing a signal responsive to a signal of a secondspecified phase received from Quad splitter 808 and responsive to asignal received from LNA 806. Each of the Baseband filters 822 832 canprovide a filtering function to a corresponding received signal.

Baseband filter 822 can be coupled with and receive a signal from Mixer820. Baseband filter 830 can be coupled with and receive a signal fromMixer 830. Each of the variable gain amplifiers (VGA) 824 834 canprovide a variable gain to a corresponding received signal. VGA 824 canbe coupled with and receive a filtered signal from Baseband filter 822.VGA 834 can be coupled with and receive a filtered signal from basebandfilter 832.

Each of the analog to digital converters (ADC) 826 836 can provide ananalog to digital conversion function to a corresponding received analogsignal. ADC 826 can be coupled with and receive a gain-modified signalfrom VGA 824. ADC 638 can be coupled with and receive a gain-modifiedsignal from VGA 834. ADC 826 can provide a baseband digital outputsignal corresponding to the first specified phase (I). ADC 836 canprovide a baseband digital output signal corresponding to the secondspecified phase (Q).

Receiver Chain Frequency Planning System Frequency Planning:

Referring to the TV band diagram 200 in FIG. 2, consider a widebanddirect-conversion receiver over the frequency range from 470 MHz to 806MHz that can span TV channels 14-69. Since Channel 37 (608-614 MHz) isnot used, the center frequency of Channel 37 can be employed as adirect-conversion carrier frequency, i.e.

f_(c)=611 MHz   (21)

A Nyquist bandwidth can be specified of

2 W=400 MHz   (22)

covering the RF signal frequencies from 411 MHz to 811 MHz. A number ofalternative ADCs with 400 MHz sampling frequency and above can be usedin an embodiment [National Semiconductor Corporation, ADC081000, 2004op. cit.], [Maxim Integrated Products, MAX108, 10/01, op. cit.], [AnalogDevices, Inc. “AD12401 Data Sheet, Rev A.”, D05649-0-4/06(A), May 2006].

Frequency-Domain Effect of Second-Order Nonlinearity:

Referring to a signal path of the receiver block diagram 800: prior tothe quadrature mixing stage comprising Mixer elements 820 830, there cantypically be a plurality of amplification stages, e.g. low noiseamplifier (LNA) and/or amplification within the mixers. In someembodiments, device nonlinearities in such amplification stages cancause spectral contamination. In order to ensure that frequency planningis adequate in the presence of such spectral contamination, consider anRF signal

s _(c)(t)=r(t)cos [2πf _(c) t+θ(t)]  (23)

corresponding to a baseband signal

s _(B)(t)=r(t)e ^(j0(t))   (24)

which is spectrally limited to [−W,W]. Taking into account devicenonlinearity, the signal after the amplification stages can be expressedas

$\begin{matrix}{{y(t)} \approx {\alpha_{0} + {\alpha_{1}{r(t)}{\cos \left\lbrack {{2\pi \; f_{c}t} + {\theta (t)}} \right\rbrack}} + {\alpha_{2}{r^{2}(t)}{\cos^{2}\left\lbrack {{2\pi \; f_{c}t} + {\theta (t)}} \right\rbrack}} + {\alpha_{3}{r^{3}(t)}{\cos^{3}\left\lbrack {{2\pi \; f_{c}t} + {\theta (t)}} \right\rbrack}}}} & (25)\end{matrix}$

where under the small-signal condition, only the second-order andthird-order nonlinearities are retained. Third-order nonlinearity isneglected since in-band third-order interference is inevitable. However,to insure against in-band second-order interference, consider thesecond-order nonlinearity term

$\begin{matrix}\begin{matrix}{{\alpha_{2}{r^{2}(t)}{\cos^{2}\left\lbrack {{2\pi \; f_{c}t} + {\theta \; (t)}} \right\rbrack}} = {\alpha_{2}{r^{2}(t)}\frac{1}{4}\left\{ {^{j{\lbrack{{2\pi \; f_{c}t} + {\theta {(t)}}}\rbrack}} + ^{- {j{\lbrack{{2\pi \; f_{c}t} + {\theta {(t)}}}\rbrack}}}} \right\}^{2}}} \\{= {\frac{\alpha_{2}}{4}\left\{ {\underset{\underset{{Center} = {2f_{c}}}{}}{\left\lbrack {s_{B}(t)} \right\rbrack^{2}^{j\; 2{\pi {({2\; f_{c}})}}t}} + \underset{\underset{{Center} = {{- 2}f_{c}}}{}}{\left\lbrack {s_{B}^{*}(t)} \right\rbrack^{2}^{j\; 2{\pi {({{- 2}\; f_{c}})}}t}} +} \right.}} \\\left. {{ce}\; 2{{s_{B}(t)}}_{{Center} = {D\; C}}^{2}} \right\}\end{matrix} & (26)\end{matrix}$

Consider Fourier transform pairs

s_(B)(t)·s_(B)(t)⇄S_(B)(f){circle around (×)}S_(B)(f)

s_(B)*(t)·s_(B)*(t)⇄S_(B)*(−f){circle around (×)}S_(B)*(−f)

s_(B)(t)·s_(B)*(t)⇄S_(B)(f){circle around (×)}S_(B)*(−f)   (27)

and since S_(B)(f) is spectrally limited to [−W,W], all the above signalproducts (in the immediately preceding equations) can be spectrallylimited to [−2 W,2 W]. The graph 900 of FIG. 9 illustrates the abovenonlinear effect. It is clear from the illustration that as long as acarrier frequency f_(c) satisfies

f_(c)≧3 W   (28)

a signal can be essentially free of second-order in-band interference.In some embodiments this condition can be satisfied by frequencyplanning, i.e.

611 MHz=f_(c)>3 W=600 MHz   (29)

Other Issues with Direct-Conversion Architecture:

Although some embodiments of a direct-conversion architecture do notsuffer an image problem as can some embodiments of a heterodynearchitecture, there can remain a number of challenges to a practicalimplementation [B. Razavi, op. cit.]. In some embodiments, LOself-mixing can create a DC offset. In some embodiments, analog basebandcircuitry can add considerable flicker noise—also called 1/f noise,since noise power can be proportional to 1/f. In some embodiments I/Qmismatch can occur if the I and Q signal paths are not preciselybalanced. Challenges of DC offset and flicker noise—which can prominentaround DC—can be addressed in some embodiments of an improved receiverarchitecture by using an empty 6 MHz signal channel, such as Channel 37of an exemplary TV band, at DC. In some embodiments, I/Q mismatch can becompensated through digital calibration techniques.

Receiver Chain Gain Planning

In light of frequency planning as discussed above, an ADC can beselected for an improved receiver embodiment. Consider using NationalSemiconductor's ADC 081000, an 8-bit 1 GHz ADC [Nat'l Semi. Corp.,DS200681, 2004, op. cit.], as previously mentioned. A receiver chainamplification calculation can be as discussed herein regards SignalAmplification, and employed for each 6 MHz TV channel. Assuming ADCoperation at a 800 MHz sampling frequency, a quantization noise per TVchannel can be expressed

n _(q) ^(dB) =N _(q) ^(dB)−10 log₁₀(800/6)≈−68 dBm   (30)

where N_(q) is quantization noise power as calculated in Equation (18).In order to scale noise contributions, RF chain gain g_(RF) can bespecified such that thermal noise exceeds the quantization noise at theADC. In other words,

n ₀ ^(dB) +F _(RF) ^(dB) +g _(RF) ^(dB) ≧n _(q) ^(dB) +X ^(dB)   (31)

Again a noise figure can be specified F_(RF) ^(dB)=6 dB and a marginX^(dB)=10 dB so that

g _(RF) ^(dB) ≧n _(q) ^(dB)+4−n ₀ ^(dB)=42 dB   (32)

An ADC can be operating at twice a specified sampling rate of 400 MHz;this can account for the discrepancy between the result shown here andthat in discussion regards Signal Amplification.

In some embodiments a receiver chain can provides 42 dB of amplificationas just described. When operating with a maximum received signal powerof −20 dBm, an amplified signal at an ADC can have a power level of

P_(Signal)=22 dBm   (33)

Amplified thermal noise at the ADC can have a power level of−89+42+6=−41 dBm. In order to have third order intermodulation (IM3)power remain below thermal noise power, according to Equation (16), arequired condition can be

$\begin{matrix}{{{3P_{Signal}^{dB}} - {2P_{{IP}\; 3}^{dB}} + \Gamma^{dB}} = \left. {P_{{IM}\; 3} < {- 41}}\Rightarrow{P_{{IP}\; 3}^{dB} > {\frac{1}{2}\left( {{3P_{Signal}^{dB}} + \Gamma^{dB} + 41} \right)}}\Rightarrow{P_{{IP}\; 3}^{dB} > {\frac{1}{2}\left( {{3 \times 22} + 0 + 41} \right)}}\Rightarrow{P_{{IP}\; 3}^{dB} > {53.5\mspace{11mu} {dBm}}} \right.} & (34)\end{matrix}$

where for simplicity, it can be assumed that Γ^(dB)=0. Such a high IP3can be difficult to realize in an embodiment.

Another potentially complicating design consideration can be that aspecified ADC has an input digitizing range of input (maximum)peak-to-peak 0.6V. A maximum input signal power for the I and Q ADCs canbe computed as

$\begin{matrix}{{{10\mspace{11mu} {\log_{10}\left( {2 \times \frac{0.3^{2}}{50} \times 10^{3}} \right)}} = {5.6\mspace{11mu} {dBm}}},} & (35)\end{matrix}$

far smaller than the amplified signal power of 22 dBm.

A Novel Double-ADC Receiver Architecture

Diagram 1100 depicts an embodiment in some detail comprising thedouble-ADC architecture of diagram 1000, and that can address someissues discussed herein; particularly challenges to realization of anembodiment. Some notable blocks are represented in diagram 1000. AnAmplification Stage 1 1004 can comprise an LNA and/or optionaladditional amplifications. In one embodiment the total gain provided bythis stage can be 15 dB (after 1-to-2 splitting) and a receiver chainnoise figure up to this point can be 5 dB. Given an exemplary maximumreceiver input signal power of −20 dBm, signal power at the output ofthis amplification stage can be −5 dBm.

Thermal noise power at the output of this amplification stage can be−89+15+5=−69 dBm. In order to maintain an IM3 power below the thermalnoise floor, a specified IP3 of Amplification Stage 1 must be largerthan −5+−5−(−69)/2=27 dBm. In some embodiments, a maximum component-wiseIP3 in this amplification stage can be somewhat higher than 27 dBm inorder to take into account losses through passive components, e.g.splitters and filters, in the stage.

A signal arriving at analog to digital converter ADC1 1006 can berepresentative of an input signal received by antenna 1002. Arepresentative input signal can be expressed as

$\begin{matrix}{{y(t)} = {{\sum\limits_{k \in \Omega}\; {{x_{k}(t)}^{j\; 2\; \pi \; f_{k}t}}} + {n(t)}}} & (36)\end{matrix}$

where x_(k)(t) and f_(k) are the baseband signal and frequency of a kthchannel respectively. The signal after ADC1 1006 sampling can beexpressed as

$\begin{matrix}\begin{matrix}{{y^{\prime}(t)} = {{\sum\limits_{k \in \Omega}\; {{x_{k}(t)}^{j\; 2\; \pi \; f_{k}t}}} + {n(t)} + {q(t)}}} \\{= {\sum\limits_{k \in \Omega}\; {\left\lbrack {{x_{k}(t)} + {n_{k}(t)} + {q_{k}(t)}} \right\rbrack ^{j\; 2\pi \; f_{k}t}}}} \\{\approx {\sum\limits_{k \in \Omega}\; {\left\lbrack {{x_{k}(t)} + {q_{k}(t)}} \right\rbrack ^{j\; 2\; \pi \; f_{k}t}}}}\end{matrix} & (37)\end{matrix}$

where q(t) is quantization noise; n_(k)(t) and q_(k)(t) are basebandequivalent thermal noise and quantization noise on Channel k; and in theapproximation, thermal noise can be ignored because thermal noise powerper channel can be approximately −106+15+5=−86 dBm; this can be farsmaller than quantization noise power per channel, i.e. −68 dBm. Themaximum input signal power to ADC1 1006, i.e. EØ|y(t)|²┘, can beapproximately −20+15=−5 dBm, which can be smaller than a maximumallowable ADC input signal power of 5.6 dBm.

In a baseband, digital filtering can be performed (by Digital Filteringelement 1008) to select one or more specified channels. After filtering,a subset of the selected channels can be selected Λ⊂Ω whose SNRs exceed25 dB. Element Digital Filtering 1008 can be adapted to provide thiscapability. A signal corresponding to the selected set of channels canbe expressed as

$\begin{matrix}{{y_{\Lambda}(t)} = {\sum\limits_{k \in \Lambda}\; {\left\lbrack {{x_{k}(t)} + {q_{k}(t)}} \right\rbrack ^{j\; 2\; \pi \; f_{k}t}}}} & (38)\end{matrix}$

A signal y_(Λ)(t) can be shown as y_(H)(t) in some figures herein; the“H” subscript indicating correspondence to relatively high powerchannels of an input signal. Two operations can be employed with thisset of channels. First, this set of channels can be sent to a digitalbaseband processing unit 1020 for decoding, since they have adequateSNRs. Second, an analog waveform can be reconstructed corresponding tothe signal y_(Λ)(t) using a DAC 1010. A reconstructed analog waveformcan be expressed as

$\begin{matrix}{{y_{\Lambda}(t)} = {{\sum\limits_{k \in \Lambda}\; {\left\lbrack {{x_{k}(t)} + {q_{k}(t)}} \right\rbrack ^{j\; 2\; \pi \; f_{k}t}}} + {p(t)}}} & (39)\end{matrix}$

where p(t) is quantization noise from the DAC 1010.

Subtracting a reconstructed waveform y_(Λ)(t) from an original signaly(t) can yield:

$\begin{matrix}{{{y(t)} - {y_{\Lambda}(t)}} = {{\sum\limits_{k \in {({\Omega - \Lambda})}}\; {{x_{k}(t)}^{j\; 2\; \pi \; {f_{k}{(t)}}}}} - {\sum\limits_{k \in \Lambda}\; {{q_{k}(t)}^{j\; 2\pi \; {f_{k}{(t)}}}}} - {p(t)} + {n(t)}}} & (40)\end{matrix}$

and is depicted as a signal comprising y_(L)(t) that can be provided bysumming node 1012 in FIG. 10, wherein y_(L)(t) corresponds to relativelylow power channels of an input signal.

Since the remaining channels belong to a set Ω-Λ, and these channels canhave signal powers less than 25 dB above the an exemplary per channelquantization noise floor of −68 dBm, a maximum signal power per channelcan be −68+25=−43 dBm. In an exemplary worst case, all of the channelscan have signal powers at −43 dBm and Ω-Λ can comprise an exemplarycomplete set of 55 TV channels. A worst-case power of the signaly(t)−y_(Λ)(t) then can be:

−43+10 log₁₀(55)≈−25 dBm   (41)

In order to provide a total RF chain amplification of 42 dB with thefirst-stage amplification already providing 15 dB gain, the second-stageamplification 1014 can be required to provide an additional 27 dB gain.In the above worst case example, a signal power at input of ADC2 1016(after second-stage amplification 1014) can be 2 dBm. Amplified thermalnoise power at input of ADC2 1016 can be −89+42+6=−41 dBm. To maintainan IM3 below the thermal noise floor, an IP3 of

${2 + \frac{2 - \left( {- 41} \right)}{2}} = {23.5\mspace{11mu} {dBm}}$

for second amplification stage 1014 can be specified.

The summing node 1012 can provide a signal comprising specifiedrelatively low-power bands and/or channels of a representative inputsignal but also comprising uncanceled residual signal attributed tospecified relatively high-power bands and/or channels. Digital filtering1018 can be adapted to substantially remove undesirable energycorresponding to specified bands and/or channels such as high-powerchannels corresponding to signal y_(H)(t). Digital filtering 1018 canprovide an advantageously filtered signal to digital baseband processing1020. In some embodiments digital baseband processing 1020 can furtherprocess and/or decode such an advantageously filtered signal and canprovide one or more individual channel signals corresponding toy_(L)(t).

In order to prevent significant noise figure degradation, quantizationnoise p(t) added by DAC 1010 can be kept small in comparison to thermalnoise n(t) in Equation (40). An exemplary DAC can provide up to 16-bitresolution at 500 MHz with an output peak-to-peak voltage swing of 1V.Examples of such DACs include Analog Devices AD9726 [Analog Devices,Inc., “AD9726 Data Sheet, Rev A”, D04540-0-11/05(A), November 2005] andMaxim MAX5888 [Maxim Integrated Products, “MAX5888 Data Sheet: 3.3V,16-Bit, 500 Msps High Dynamic Performance DAC with Differential LVDSInputs”, 19-2726; Rev 3; 12/03]. A quantization noise power for a 15-bitDAC can be expressed

$\begin{matrix}{{{E\left\lbrack {{p(t)}}^{2} \right\rbrack} = {{10\mspace{11mu} {\log_{10}\left\lbrack {2 \times \frac{\left( {1/2^{15}} \right)^{2}}{12}\frac{10^{3}}{50}} \right\rbrack}} \approx {{- 85}\mspace{11mu} {dBm}}}},} & (42)\end{matrix}$

which is less than a specified thermal noise floor of −89+15+5=−69 dBm.

Diagram 1100 shows in some detail a RF block diagram of an exampledirect-conversion double-ADC receiver. Many suitable components for anexemplary embodiment are identified herein, by way of non-limitingexample.

The system of diagram 1100 comprises individual processing elements wellknown in the art and/or described herein. Each of these elements isgenerally identified herein with a name and/or abbreviation thatcorresponds to its well known and/or herein described function. Analogfilters comprise BandPass 1108, LowPass1 1124 1174, and ReConstruction1130 1180. Digital filtering and/or other specified digital signalprocessing comprises Digital Filtering 1127 1177. Gain modifyingelements comprise low noise amplifiers LNA1 1106 and LNA2 1110,automatic gain control AGC1 1122 1172 and AGC2 1134 1184. Analog todigital converters comprise AD 1126 1176 1136 1186. Digital to analogconverters comprise DA 1128 1178.

Splitters comprise elements 1112 and 1116. Mixers comprise elements 1120and 1170. Summing nodes comprise elements 1132 and 1182. Delaycompensation elements comprise Delay Comp. 1125 1175.

Delay elements comprise Phase Shift 1118.

LNA1 1106 can be selectably coupled with Antenna 1102 via switch 1104.When so coupled, LNA1 1106 can receive a signal from Antenna 1102.BandPass 1108 can be coupled with and receive a signal from LNA1 1106.LNA2 can be coupled with and receive a signal from BandPass 1108.

Splitter 1112 can be coupled with and receive a signal from LNA2 1110.Mixer 1120 can be coupled with and receive a signal from Splitter 1112.Mixer 1120 can be coupled with and receive a signal from Splitter 1116.

Mixer 1170 can be coupled with and receive a signal from Splitter 1112.Mixer 1170 can be coupled with and receive a signal from PhaseShift1118. PhaseShift 1118 can be coupled with and receive a signal fromSplitter 1116. Splitter 1116 can be coupled with and receive a signalfrom an oscillator LO 1114.

AGC1 1122 can be coupled with and receive a signal from Mixer 1120.

LowPass1 1124 can be coupled with and receive a signal from AGC1 1122.

Delay Comp. 1125 can be coupled with and receive a signal from LowPass11124.

Summing node 1132 can be coupled with and receive a signal from DelayComp. 1125.

AD 1126 can be coupled with and receive a signal from LowPass1 1124.

Digital Filtering 1127 can be coupled with and receive a signal from AD1126.

DA 1128 can be coupled with and receive a signal from Digital Filtering1127.

ReConstruction 1130 can be coupled with and receive a signal from DA1128.

Summing node 1132 can be coupled with and receive a signal fromReConstruction 1130.

AGC2 1134 can be coupled with and receive a signal from Summing node1132.

AD 1136 can be coupled with and receive a signal from AGC2 1134.

AD 1136 can provide a baseband in-phase component signal.

AGC1 1172 can be coupled with and receive a signal from Mixer 1170.

LowPass1 1174 can be coupled with and receive a signal from AGC1 1172.

Delay Comp. 1175 can be coupled with and receive a signal from LowPass11174.

Summing node 1182 can be coupled with and receive a signal from DelayComp. 1175.

AD 1176 can be coupled with and receive a signal from LowPass1 1174.

Digital Filtering 1177 can be coupled with and receive a signal from AD1176.

DA 1178 can be coupled with and receive a signal from Digital Filtering1177.

ReConstruction 1180 can be coupled with and receive a signal from DA1178.

Summing node 1182 can be coupled with and receive a signal fromReConstruction 1180.

AGC2 1184 can be coupled with and receive a signal from Summing node1182.

AD 1186 can be coupled with and receive a signal from AGC2 1184.

AD 1186 can provide a baseband quadrature component signal.

Exemplary digital-analog conversion devices can be specified: NationalSemiconductor's ADC081000 [Nat'l Semi. Corp., DS200681, 2004, op. cit.],an 8-bit 1 GHz ADC, and Analog Devices' AD9726 [Analog Devices, Inc.,D04540-0-11/05(A), November 2005, op. cit.], a 16-bit 600 MHz DAC. Asshown in Diagram 1100, a first amplification stage comprises LNAs,bandpass filters, splitters, mixers, variable gain amplifiers, andlowpass filters, with a total gain of 15 dB and a noise figure ofapproximately 5 dB. Exemplary system components and a cascaded gainanalysis are shown in the following table.

]Note that because of losses due to the passive components, e.g.splitters and filters, in some embodiments one or more amplifiers can beneeded in a first amplification stage. In some embodiments a secondamplification stage can consist of variable gain amplifiers. An IP3calculation for a second amplification stage can assume a maximum inputsignal power of −25 dBm, as discussed herein.

Max. Output output Vendor: NF NF Gain power IP3 DR Name Part (dB) (dB)(dB) (dBm) (dBm) (dB) LNA1 Mini- 3.5 3.5 12 −8 47 110 Circuits: HELA-10B Bandpass TBD 3 3.6 −3 −11 ∞ ∞ LNA2 Mini- 3.5 3.9 12 1 47 92Circuits: HELA- 10B Splitter Mini- 4 3.9 −4 −3 ∞ ∞ Circuits: ZFSC- 2-2Mixer Mini- 8 4.1 −8 −11 30 82 Circuits: ZFY-2 AGC1 Linear 7 4.9 14 3 4788 Tech: LT5514 Lowpass1 TBD 8 4.9 −8 −5 ∞ ∞ AGC2 Linear 7 5.1 27 2 4790 Tech: LT5514

The above discussions and analysis show a wideband direct-conversiondouble-ADC receiver using exemplary hardware components can provideenabling system performance levels for embodiments of a TV-bandcognitive radio system, and, can allow simultaneous decoding ofessentially all of the TV channels in a designated spectrum.

A conventional single-channel heterodyne receiver can be considered as areference and a cost-effective alternative to the embodiments above. Aheterodyne receiver can use progressive filtering in an analog domain inorder to improve channel selectivity. Although such a receiver may nothave the capability of simultaneous decoding of multiple channels,neither does it require high-speed ADCs. It can also be instructive tocompare the single-channel performance of the heterodyne receiver withthat of the wideband receiver.

IP3 requirements for realizable embodiments of a double-ADC architecturecan be relatively stringent. In some embodiments, the worst-case IM3interference can be allowed to be higher than the thermal noise floor.

Remaining interference can then be removed in a digital domain throughdistortion compensation techniques.

A Reference Heterodyne Receiver Design

RF system design embodiments of a conventional single-channel heterodynereceiver can serve as a reference point and as an alternative towideband direct-conversion receiver embodiments discussed herein.

Heterodyne Frequency Planning

Frequency planning for a heterodyne receiver can present further designchallenges than that of a direct-conversion receiver. For someembodiments of a heterodyne receiver, two frequency translations can berequired, i.e. from RF to IF and from IF to baseband (although frequencytranslation between IF and baseband can be achieved in some embodimentsemploying direct IF sampling and/or digital frequency synthesis). One ofthe key design issues of a heterodyne receiver embodiment can bespecification of an intermediate frequency (IF).

IF Filtering:

As discussed herein regards Receiver Architecture Choices, a mainpurpose of an IF stage in a heterodyne receiver can be to providechannel selection filtering, because effective filtering can be moreeasily accomplished at a relatively low IF frequency than at arelatively high RF frequency. Availability of off-the-shelf IF filterscan contribute to a practical selection and/or specification of an IFfrequency.

A surface acoustic wave (SAW) filter can be a typical choice for IFchannel selection. Some embodiments of exemplary commercially availableSAW filters can have specified center frequencies of 40 MHz, 70 MHz, and140 MHz [16,17].

Image Rejection:

Referring to Diagram 600 of FIG. 6: Mixer 614 can be a second-orderdevice, that is, a device that does not differentiate between positiveand negative frequencies. Consequently, after mixing, a down-convertedsignal can contain both an intended signal and an image signal asillustrated in Diagram 1200 of FIG. 12.

Mathematically, an intended signal can be represented as

R_(s)(t)cos [2πf_(c)t+φ_(s)(t)]  (43)

which can be band-limited to [f_(c)−W,f_(c)+W]; an image signal can berepresented as

R_(i)(t)cos [2πf_(i)t+φ_(i)(t)]  (44)

and mixing can use a tone signal

cos(2πf_(LO)t)

A mixing operation can be expressed as

$\begin{matrix}{{\left\{ {{{R_{s}(t)}{\cos \left\lbrack {{2\pi \; f_{c}t} + {\varphi_{s}(t)}} \right\rbrack}} + {{R_{i}(t)}{\cos \left\lbrack {{2\pi \; f_{i}t} + {\varphi_{i}(t)}} \right\rbrack}}} \right\} \times {\cos \left( {2\pi \; f_{LO}t} \right)}} = {\underset{\underset{1}{}}{\frac{1}{2}{R_{s}(t)}{\cos \left\lbrack {{2{\pi \left( {f_{c} - f_{LO}} \right)}t} + {\varphi_{s}(t)}} \right\rbrack}} + \underset{\underset{2}{}}{\frac{1}{2}{R_{s}(t)}{\cos \left\lbrack {{2{\pi \left( {f_{c} + f_{LO}} \right)}t} + {\varphi_{s}(t)}} \right\rbrack}} + \underset{\underset{3}{}}{\frac{1}{2}{R_{i}(t)}{\cos \left\lbrack {{2{\pi \left( {f_{i} - f_{LO}} \right)}t} + {\varphi_{i}(t)}} \right\rbrack}} + \underset{\underset{4}{}}{\frac{1}{2}{R_{i}(t)}{\cos \left\lbrack {{2{\pi \left( {f_{i} + f_{LO}} \right)}t} + {\varphi_{i}(t)}} \right\rbrack}}}} & (45)\end{matrix}$

A filtering operation [f_(c)−f_(LO)−W,f_(c)−f_(LO)+W] can be applied tothe signal after mixing, whereupon the second and fourth term in theabove expression can essentially vanish. However, for an image signal at

f _(i)=2f _(LO) −f _(c)   (46)

the third term above can become

$\begin{matrix}{{\frac{1}{2}{R_{i}(t)}{\cos \left\lbrack {{2{\pi \left( {f_{LO} - f_{c}} \right)}t} + {\varphi_{i}(t)}} \right\rbrack}} = {\frac{1}{2}{R_{i}(t)}{\cos \left\lbrack {{2{\pi \left( {f_{c} - f_{LO}} \right)}t} - {\varphi_{i}(t)}} \right\rbrack}}} & (47)\end{matrix}$

In other words, this signal can be in the same band, i.e.[f_(c)−f_(LO)−W,f_(c)−f_(LO)+W], as an intended signal after mixing(first term). One way to resolve the problem is to apply an imagerejection (IR) filter 1202 before mixing as shown in the graph 1200 ofFIG. 12 so that an image signal at 2f_(LO)−f_(c) can be rejected beforea signal enters a mixer.

Frequency Planning:

For some embodiments, an intended signal can be in a specified band suchas [470,806] MHz. An ideal image rejection filter can be a brick-wallfilter around a specified band. Suppose such an ideal IR (imagerejection) filter is used in an embodiment: essentially full pass in[470,806] MHz and essentially infinite rejection otherwise. f_(c),f_(LO), and f_(IF) can be the carrier, LO, and IF frequencies,respectively. To have image-free mixing in some embodiments, thefollowing conditions must be essentially met

2f _(LO) −f _(c)<470 or 2f _(LO) −f _(c)>806   (48)

f _(c) −f _(LO) =+f _(IF) or f _(c) −f _(LO) =−f _(IF)   (49)

Since 2f_(LO)−f_(c) is an image frequency, the first condition above cansuggest that the image frequency must stay in a rejection band of an IRfilter. The second condition can be expressed as |f_(c)−f_(LO)|=f_(IF),where the absolute value is due to the properties of a realizable signalmixer.

Given IF frequency candidates of 40 MHz, 70 MHz, and 140 MHz, the threepossible IF frequencies can be substituted in the above conditions andthe systems solved for possible solutions. Solutions can beadvantageously perceived graphically, as shown in graphs 1300, 1400, and1500.

Graph 1300 corresponds to a condition (f_(IF)=140 MHz). Line A 1302corresponds to (2f_(LO)−f_(c)=470). Line B 1304 corresponds to(2f_(LO)−f_(c)=806). Line C 1306 corresponds to (f_(c)−f_(LO)=140). LineD 1308 corresponds to (f_(c)−f_(LO)=−140).

A portion of line C 1306 shown in a region below line A 1302(corresponding to (2f_(LO)−f_(c)<470)) can be part of a solution, and, aportion of line D 1308 shown in a region above line B 1304(corresponding to (2f_(LO)−f_(c)>806)) can also be part of a solution.By way of non-limiting example, f_(c)=500 MHz is shown to be in SolutionRegion_1 1310 and with an f_(LO)=360 MHz, an image is thereby at 220 MHzand within a rejection region of the IR filter. Since each solutionregion can cover a part of the input signal frequency range (e.g.Solution Region_1 1310 can cover 750 MHz and below and Solution Region_21312 can cover 543 MHz and above), both regions can be necessary for anembodiment comprising an entire exemplary input frequency range, i.e.[470,806] MHz. Thus the constraints of Graph 1300 can lead to apractical realization for single-stage image-free IF mixing in someembodiments.

Graph 1400 corresponds to a condition (f_(IF)=70 MHz). Line A 1402corresponds to (2f_(LO)−f_(c)=470). Line B 1404 corresponds to(2f_(LO)−f_(c)=806). Line C 1406 corresponds to (f_(c)−f_(LO)=70). LineD 1308 corresponds to (f_(c)−f_(LO)=−70).

Graph 1400 shows a Gap 1414 between solution regions 1410 1412,corresponding to a region wherein image-free mixing can not occur insome embodiments. For the constraints corresponding to graph 1400, someembodiments employing 70 MHz IF filters for single-stage image-free IFmixing can fail to provide a solution for an entire exemplary TV band[470,806] MHz.

A similar analysis can show that some embodiments employing 40 MHz IFfilters under such constraints can fail to provide a solution coveringan entire exemplary TV band [470,806] MHz.

The conditions for Graph 1300 and Graph 1400 correspond to an idealbrick-wall IR filter over the signal band. In practice, typical filterembodiments can have gradual edge roll-offs. Thus in some embodimentsmargins can be employed at IR filter edges in order to provide aspecified level of image rejection. By way of non-limiting example, a100-MHz margin can be added to each side of an IR filter in order toaccount for edge roll-offs. An image rejection region can then be

2f _(LO) −f _(c)<370 and 2f _(LO) −f _(c)>906   (50)

Graph 1500 shows a solution for the conditions discussed. Line A 1502corresponds to (2f_(LO)−f_(c)=370). Line B 1504 corresponds to(2f_(LO)−f_(c)=906). Line C 1506 corresponds to (f_(c)−f_(LO)=140). LineD 1508 corresponds to (f_(c)−f_(LO)=−140).

An advantageous overlap between Solution Region_1 1510 and SolutionRegion_2 1512 can be relatively smaller than the overlap shown in Graph1300. By way of non-limiting example, 650 MHz can be a cutoff frequency.For exemplary TV channels 14 (center 473 MHz) to 43 (center 647 MHz), anLO frequency can be

f _(LO) =f _(c)−140   (51)

and for exemplary TV channels 44 (center 653 MHz) to 69 (center 803MHz), an LO frequency can be

f _(LO) =f _(c)+140   (52)

Gain Planning

Graph 1600 of FIG. 16 depicts the response of an exemplary SAW filter[Vectron International, “Surface Acoustic Wave (SAW) Products”http://www.vectron.com/products/saw/saw.htm]. The filter has a specifiedpassband of approximately 6 MHz. The specified rejection for two 6 MHzchannels adjacent to the pass band can be specified as at least 15 dB(due to the finite roll-offs at filter edges as shown in the figure).Specified rejection for the channels not adjacent to the pass band canbe at least 50 dB. The filter has a specified insertion loss of 22.5 dB.

A SAW filter channel rejection mask as shown in FIG. 17 can be assumed.A target channel k has 0 dB rejection. Rejection for adjacent channelsk±1 is specified as 15 dB. Rejection for all other channels is specifiedas 40 dB. Some embodiments of SAW filters are able to essentially meetthe specified requirements of such a rejection mask.

As discussed regards Receiver Chain Gain Planning, a per channel thermalnoise floor n₀ ^(dB) of −106 dBm can be specified, a per channelquantization noise floor n_(q) ^(dB) of −68 dBm can be specified, and areceiver chain noise figure F_(thrmRF) ^(dB) of 6 dB can be specified. ASNR degradation due to the quantization noise can be required to be 0.46dB, corresponding to an X^(dB) value of 10 dB. A total RF chainamplification requirement can be obtained from the following SNRequation

$\begin{matrix}{{SNR}_{Final}^{dB} = {{10\mspace{11mu} \log_{10}\frac{g_{RF}P_{k}}{{g_{RF}n_{0}F_{RF}} + n_{q}}} = {\min \left\{ {{30\mspace{11mu} {dB}},{P_{k}^{dB} - \left( {n_{0}^{dB} + F_{RF}^{dB}} \right) - 0.46}} \right\}}}} & (53)\end{matrix}$

where SNR_(Final) ^(dB) is SNR measured at the baseband input; g_(RF) istotal RF chain gain; and P_(k) is input (received) signal power of atarget channel. It can be appreciated that the SNR ceiling can be set to30 dB in order to meet specified performance levels. Graph 1800 of FIG.18 depicts a graphical solution to Equation (53). As shown in thefigure, for high input power levels the gain required can be reduced asa result of a SNR ceiling at 30 dB.

A total input signal power can be expressed

$\begin{matrix}{P_{k} + \left( {P_{k - 1} + P_{k + 1}} \right) + {\sum\limits_{l \in \Omega^{\prime}}\; P_{l}}} & (54)\end{matrix}$

where Ω′ can be a whole channel set excluding channels k and k±1.Assuming a SAW filter rejection mask as shown in Diagram 1700, after SAWfiltering, a total signal power can be expressed:

$\begin{matrix}{P_{k} + {10^{- \frac{15}{10}}\left( {P_{k - 1} + P_{k + 1}} \right)} + {10^{- \frac{40}{10}}{\sum\limits_{l \in \Omega^{\prime}}\; P_{l}}}} & (55)\end{matrix}$

and a total signal power at an ADC (after RF chain amplification) can beexpressed:

$\begin{matrix}{g_{RF}\left\lbrack {P_{k} + {10^{- \frac{15}{10}}\left( {P_{k - 1} + P_{k + 1}} \right)} + {10^{- \frac{40}{10}}{\sum\limits_{l \in \Omega^{\prime}}\; P_{l}}}} \right\rbrack} & (56)\end{matrix}$

A condition can be imposed that the signal powers of the two adjacentchannels satisfy

$\begin{matrix}{{10\mspace{11mu} \log_{10}\frac{P_{k - 1} + P_{k + 1}}{P_{k}}} < A^{dB}} & (57)\end{matrix}$

where A^(dB) can be a maximum specified adjacent channel powerdifferential, e.g. 40 dB. Without this condition, adjacent channelleakage could overwhelm a signal in a desired channel (e.g. referring tothe DTV transmission mask in Diagram 2100). Assuming a maximum totalinput signal power of −20 dBm, signal power at the ADC can have an upperbound P_(Bound) such that:

$\begin{matrix}{{{g_{RF}\left\lbrack {P_{k} + {10^{- \frac{15}{10}}\left( {P_{k - 1} + P_{k + 1}} \right)} + {10^{- \frac{40}{10}}{\sum\limits_{l \in \Omega^{\prime}}\; P_{l}}}} \right\rbrack} < {g_{RF}\left\lbrack {P_{k} + {10^{- \frac{15}{10}}{AP}_{k}} + {10^{- \frac{40}{10}}{\sum\limits_{l \in \Omega^{\prime}}\; P_{l}}}} \right\rbrack} < {g_{RF}\left\lbrack {P_{k} + {10^{- \frac{15}{10}}10^{\frac{40}{10}}P_{k}} + {10^{- \frac{40}{10}}10^{- \frac{20}{10}}}} \right\rbrack}} = P_{Bound}} & (58)\end{matrix}$

where in the second inequality A^(dB) can be specified as 40 dB and aconstraint that Σ_(lεΩ′)P_(l) is less than −20 dBm can be employed. Thisupper bound is plotted in Diagram 1800.

According to Diagram 1800, a maximum possible signal power at an ADC canbe less than −3 dBm. A thermal noise power, shown as Final noise powerin Diagram 1800, at this point can be −58 dBm. An IP3 requirement for anamplifier in the signal chain just prior to an ADC can then be expressed

$\begin{matrix}{{{- 3} + \frac{{- 3} - \left( {- 58} \right)}{2}} = {24.5\mspace{11mu} {dBm}}} & (59)\end{matrix}$

In some embodiments, a 140 MHz IF signal can be down-converted to abaseband using a conventional down-conversion approach as shown inDiagram 600. Alternative embodiments can employ direct IF sampling withdigital down-conversion. In some embodiments, ADCs with 400 MHz and/orgreater sampling frequencies [8,9,12] can be used to perform direct IFsampling.

In some embodiments, an LNA and a mixer can provide enough gain toovercome a SAW filter insertion loss, which can have a typical value of20 dB. Exemplary low-loss SAW filters (with 10 dB insertion loss) areavailable [Integrated Device Technology, Inc., “Saw Filter Products”,http://www.idt.com/?id=3350]. Employing such SAW filters in someembodiments can contribute to relaxing a specified amplificationrequirement on an LNA and mixer. As shown in Diagram 1800, an RF chaincan be specified to provide an adjustable gain range of 60 dB, i.e. from−20 dB to +40 dB. In some embodiments an LNA and mixer can provide aswitchable gain step of 20 dB. One or more amplifier(s) following a SAWfilter can then provide an adjustable gain of between 0 and 40 dB. Thisgain can be combined with a 20 dB LNA-mixer gain step and can provide aspecified 60 dB dynamic range. Automatic gain control (AGC) can beemployed to ensure correct gain levels at an LNA and mixer andgain-adjustable amplifier(s), under the condition of varying inputsignal powers, in order to achieve optimal system performance.

Example System:

Diagram 1900 depicts a block diagram embodiment of an examplesingle-channel heterodyne receiver wherein exemplary cascaded SAWfilters can be used to achieve a desired level of channel selectivity.

Many exemplary processing components are identified.

The system of diagram 1900 comprises individual processing elements wellknown in the art and/or described herein. Each of these elements isgenerally identified herein with a name and/or abbreviation thatcorresponds to its well known and/or herein described function. Analogfilters comprise BandPass 1908 and LowPass 1926. Exemplary SAW filterscomprise IF Filter1 1920 and IF Filter2 1922. Gain modifying elementscomprise low noise amplifiers LNA1 1906 and LNA2 1910, automatic gaincontrol AGC1 1918 and AGC2 1924. Analog to digital converters compriseAD 1928. Mixers comprise Mixer 1916. Attenuators comprise Attenuator1912.

LNA1 1906 can be selectably coupled with Antenna 1902 via switch 1904.When so coupled, LNA1 1906 can receive a signal from Antenna 1902.BandPass 1908 can be coupled with and receive a signal from LNA1 1906.LNA2 1910 can be coupled with and receive a signal from BandPass 1908.Attenuator 1912 can be coupled with and receive a signal from LNA2 1910.Mixer 1916 can be coupled with and receive a signal from Attenuator1912. Mixer 1916 can be coupled with and receive a signal from Buffer1914.

Buffer 1914 can provide an LO signal, as from an oscillator.

AGC1 1918 can be coupled with and receive a signal from Mixer 1916. IFFilter1 1920 can be coupled with and receive a signal from AGC1 1918. IFFilter2 1922 can be coupled with and receive a signal from IF Filter11920. AGC2 1924 can be coupled with and receive a signal from IF Filter21922. LowPass 1926 can be coupled with and receive a signal from AGC21924. AD 1928 can be coupled with and receive a signal from LowPass1926.

AD 1186 can provide a baseband component signal.

In some embodiments, an exemplary ADC, Analog Devices' AD12401 [AnalogDevices, Inc. AD12401, May 2006, op. cit.], a 12-bit 400 MHz ADC, can beused for direct IF sampling. The following table shows a system gainanalysis. An exemplary SAW filter can have adjacent channel rejection of8 dB and “Max. output power” can be reduced accordingly at the output ofeach SAW filter. Thus for some exemplary embodiments, a resultingoverall system noise figure can be computed to be about 5.2 dB.

Max. Output output Vendor: NF NF Gain power IP3 DR Name Part (db) (dB)(dB) (dBm) (dBm) (dB) LNA1 Mini- 3.5 3.5 12 −8 47 110 Circuits: HELA-10B Bandpass TBD 3 3.6 −3 −11 ∞ ∞ LNA2 Mini- 3.5 3.9 12 1 47 92Circuits: HELA- 10B Attenuator TBD 4 3.9 −4 −3 ∞ ∞ Mixer Mini- 8 4.1 −8−11 30 82 Circuits: ZFY-2 AGC1 Linear 7 4.9 17 6 47 82 Tech: LT5514 IFFilter 1 Sawtek: 6 4.9 −6 −8 ∞ ∞ 854913 IF Filter 2 Sawtek: 6 4.9 −6 −22∞ ∞ 854913 AGC2 Linear 7 5.2 31 9 47 76 Tech: LT5514 Lowpass TBD 3 5.2−3 6 ∞ ∞

Transmitter Architecture

Diagram 2000 depicts an embodiment of a wideband direct-conversiontransmitter comprising a similar structure as that of the widebanddirect-conversion receiver of Diagram 800. ADC elements 826 836 and DACelements 2026 2036 have corresponding positions within the depictedsignal processing chains, respectively. The position of LNA 806corresponds to that of PA 2006. Essentially the same frequency planningapproaches as discussed regarding direct-conversion receiver embodimentscan be employed regarding direct-conversion transmitter embodiments. Insome embodiments, a mixing stage in diagram 2000 can perform anup-conversion function; the mixing stage can comprise Mixer 2020 andMixer 2030, and Quad splitter 2008.

Each of the digital to analog converters DAC 2026 2036 can provide adigital to analog conversion function to a corresponding received analogsignal.

Each of the converters DAC 2026 2036 can be provided with a basebandcomponent signal (I and Q, respectively).

Each of the Baseband filters 2022 2032 can provide a filtering functionto a corresponding received signal.

Baseband filter 2022 can be coupled with and receive a signal from DAC2026. Baseband filter 2032 can be coupled with and receive a signal fromDAC 2036.

Oscillator LO 2010 can provide a signal that can be a tone signal at aspecified frequency.

Quad splitter 2008 can provide a quadrature splitting function to areceived signal, thereby providing an in-phase (I) and a quadrature (Q)signal.

Quad splitter 2008 can be coupled with and receive a signal from LO2010.

Mixer 2020 can be coupled with and receive a signal of a first specifiedphase from Quad splitter 2008.

Mixer 2020 can be coupled with and receive a filtered signal fromBaseband filter 2022.

Mixer 2030 can be coupled with and receive a signal of a secondspecified phase from Quad splitter 2008.

Mixer 2030 can be coupled with and receive a filtered signal fromBaseband filter 2032.

Mixer 2020 can provide a mixing function, providing a signal responsiveto a signal received from Quad splitter 2008 and responsive to a signalreceived from Baseband filter 2022. Similarly,

Mixer 2030 can provide a mixing function, providing a signal responsiveto a signal of a second specified phase received from Quad splitter 2008and responsive to a signal received from Baseband filter 2032.

Tx Power Control 2007 can provide a transmission power control functionto a received signal and/or received combination of signals. Atransmission power control function can comprise a selectably adjustablegain and/or predistortion and/or any other known and/or convenienttransmission power control techniques.

Tx Power Control 2007 can be coupled with and receive a combination ofsignals from Mixer 2020 and Mixer 2030. In some embodiments, a combinerelement can be employed to combine signals from Mixer 2020 and Mixer2030.

A power amplifier PA 2006 can provide a power amplification function toa received signal.

PA 2006 can be coupled with and receive a signal from Tx Power Control2007.

RF filter 2004 can provide a filtering function to a received signal.

RF filter 2004 can be coupled with and receive a power-amplified signalfrom PA 2006.

Antenna 2002 can provide an antenna transmission function to a receivedsignal.

Antenna 2002 can be coupled with and receive a filtered signal from RFfilter 2004.

Antenna 2002 can provide transmission of a signal responsive to afiltered signal received from RF filter 2004.

A maximum transmission power can be limited to 1 W or 30 dBm accordingto the NPRM [FCC, May 2004, op. cit.]. Considering the same exemplary16-bit DAC as previously discussed, a maximum signal power out of theDAC can be calculated

$\begin{matrix}{{10\mspace{11mu} {\log_{10}\left( {2 \times \frac{0.5^{2}}{50} \times 10^{3}} \right)}} = {10\mspace{11mu} {dBm}}} & (60)\end{matrix}$

Alternative modulation schemes can have varying backoff requirements.For example, if OFDM is used, a backoff of 2.5 bits translating into apower loss of 15 dB can be required. A maximum signal power out of a DAC2026 2036 can then be −5 dBm. A total transmitter RF chain amplificationof 35 dB can then be needed before a signal reaches the antenna. A PA2006 can typically provide 20 dB to 30 dB of gain. Additionalamplification stages can then be needed between a PA 2006 and a DAC(2026 and/or 2036).

Transmitter power control (TPC) can be helpful in improving wirelesssystem capacity. TPC can be achieved using a variable gain amplifier2007 as shown in Diagram 2000. Alternatively, by employing a DAC with anample number of bits (16), transmission power control can also beachieved using the DAC. For example, the top 8 bits of a DAC output canbe dedicated to TPC. This can provide a total of 8×6=48 dB TPC range. Insome embodiments, the remaining 8 DAC bits can be used for OFDMmodulation: 2.5 bits for backoff and 5.5 bits for OFDM signalrepresentation.

The FCC may adopt the same DTV transmit mask as shown in Graph 200 for aTV-band cognitive radio. Given a modulation format, using the spectrummask, linearity requirements of RF components can be derived.

Since a PA can provide a last amplification stage, transmit chainnonlinearity can be dominated by that of the PA. Digital pre-distortioncan be used for PA linearization. Digital pre-distortion techniques canbe considered in a baseband system design.

Diagram 2200 depicts a block diagram in some detail of an exampleembodiment of a wideband direct-conversion transmitter architectureessentially as depicted in Diagram 2000. In some embodiments, anexemplary integrated wideband up-converter HMC497LP4 from HittiteMicrowave can be used for signal up-conversion. In some embodiments, anexemplary Mini-Circuits ZHL-3010 amplifier can be used as a PA driver.In some embodiments, an Ophir 5303039A PA can have an output IP3 of 56dBm and can provide an output power of 36 dBm with out-of-band emissionlevel at −4 dBm. Notably, in some embodiments, every 1 dB reduction intransmission power can result in a 2 dB reduction in out-of-bandemissions.

Transmission power control can be employed in some embodiments to reduceout-of-band emissions.

The system of diagram 2200 comprises individual processing elements wellknown in the art and/or described herein. Each of these elements isgenerally identified herein with a name and/or abbreviation thatcorresponds to its well known and/or herein described function. Analogfilters comprise BandPass 2204 and LowPass 2222 2232. Gain modifyingelements comprise Gain 2223 2233, PA 2206, and VGA 2207. Digital toanalog converters comprise DAC 2226 2236. An Upconverter 2209 cancomprise splitter/combiners, mixers, and a delay element. In someembodiments an Upconverter 2209 can be adapted to combine received (I)and (Q) baseband component signals into a signal having a modulating orcarrier signal at the frequency of a received LO signal; hence“upconversion”. In some embodiments VGA 2207 can be adapted to providetransmission power control.

Gain 2223 can be coupled with and receive a signal from DAC 2226.LowPass 2222 can be coupled with and receive a signal from Gain 2223.Upconverter 2209 can be coupled with and receive a baseband componentsignal from LowPass 2222. Gain 2233 can be coupled with and receive asignal from DAC 2236. LowPass 2232 can be coupled with and receive asignal from Gain 2233. Upconverter 2209 can receive an LO signal.

VGA 2207 can be coupled with and receive a modulated signal fromUpconverter 2209. PA 2206 can be coupled with and receive a signal fromVGA 2207. BandPass 2204 can be coupled with and receive a signal from PA2206. Antenna 2202 can be selectably coupled via Switch 2203 withBandPass 2204. When so coupled, Antenna 2202 can receive a signal fromBandPass 2204 When so coupled, Antenna 2202 can provide transmission ofa signal responsive to a filtered signal received from BandPass 2204.

Baseband System Analysis:

A baseband system design is described herein.

FFT/IFFT-based digital filtering and reconstruction for arbitrarychannel rejection:

A double-ADC architecture for a wideband direct-conversion TV-bandcognitive radio receiver is herein described. An enabling function forthis architecture can be channel rejection through digital filtering andreconstruction. Herein described is such a channel rejection method froma baseband perspective.

Channel filtering can be accomplished using a common digital filter,e.g. a raised-cosine filter. It can also be achieved using an FFT andIFFT pair in combination. The latter approach can be especiallyefficient in simultaneous filtering of multiple channels, as required insome embodiments.

Herein described are derivations of a continuous-time version of theoperations of FFT/IFFT based filtering and reconstruction. Equivalentdiscrete-time version of the operations are subsequently described

Channel Rejection Analysis:

Referring to Equation (37), suppose a total signal is

$\begin{matrix}{{y(t)} = {{\sum\limits_{k \in \Omega}\; {y_{k}(t)}} = {\sum\limits_{k \in \Omega}\; {\left\lbrack {{x_{k}(t)} + {q_{k}(t)}} \right\rbrack ^{{j2}\; \pi \; f_{k}t}}}}} & (61)\end{matrix}$

from which a designated set of channels are to be rejected

$\begin{matrix}{\sum\limits_{l \in \Lambda}\; {y_{l}(t)}} & (62)\end{matrix}$

An input signal can be truncated using a time-domain window w(t):

y _(l)(t)=w(t)y(t)   (63)

which can then be “FFT'd” in order to generate a frequency-domain signalrepresentation

$\begin{matrix}{{Y_{1}(f)} = {{F\left\lbrack {y_{1}(t)} \right\rbrack} = {{W(f)} \otimes {\sum\limits_{k \in \Omega}\; {Y_{k}(f)}}}}} & (64)\end{matrix}$

To retrieve the signal on a particular channel l ε Λ, a frequency-domainrectangular window on Y₁(f) can be applied:

Y ₁(f)=Π_(2C)(f−f_(l))Y ₁(f)   (65)

where Π_(2C)(f) is a rectangular window over the frequency range [−C,C]with

C=3 MHz+Δ  (66)

and Δ being the excess filter bandwidth. For all the channels in Λ, then

$\begin{matrix}{{Y^{\prime}(f)} = {{\sum\limits_{l \in \Lambda}\; {Y_{l}(f)}} = {\left\lbrack {\sum\limits_{l \in \Lambda}\; {\Pi_{2C}\left( {f - f_{l}} \right)}} \right\rbrack {Y_{1}(f)}}}} & (67)\end{matrix}$

Note that for simplifying assumption that the channels in Λ aredisjoint. In the case of contiguous channels, an overall rectangularwindow can be applied to the contiguous channels. The signal Y′(f) canthen be transformed to time domain in order to generate y′(t) as areconstructed version of the signals on the channels in Λ.

In order to evaluate how much rejection can be achieved, the signaly′(t) can be subtracted from y₁(t):

$\begin{matrix}\begin{matrix}{{{y_{1}(t)} - {y^{\prime}(t)}} = {{{w(t)}{y(t)}} - {y^{\prime}(t)}}} \\{= {{{w(t)}\left\lbrack {\sum\limits_{k \in {({\Omega - \Lambda})}}\; {y_{k}(t)}} \right\rbrack} + \left\lbrack {{{w(t)}{\sum\limits_{l \in \Lambda}\; {y_{l}(t)}}} - {y^{\prime}(t)}} \right\rbrack}}\end{matrix} & (68)\end{matrix}$

So the remaining signal power on the channels in Λ can be expressed:

$\begin{matrix}{\int_{- \infty}^{\infty}{{E\left\lbrack {{{{w(t)}{\sum\limits_{l \in \Lambda}\; {y_{l}(t)}}} - {y^{\prime}(t)}}}^{2} \right\rbrack}\ {t}}} & (69)\end{matrix}$

Since a similar amount of rejection can be applied to any individualchannel l ε Λ, consider that Λ only contains one channel l as asimplifying assumption. Using Parseval's theorem

$\begin{matrix}{{\int_{- \infty}^{\infty}{{E\left\lbrack {{{{w(t)}{y_{l}(t)}} - {y_{l}(t)}}}^{2} \right\rbrack}\ {t}}} = {\int_{- \infty}^{\infty}{{E\left\lbrack {{{{W(f)} \otimes {Y_{l}(f)}} - {Y_{l}(f)}}}^{2} \right\rbrack}\ {f}}}} & (70)\end{matrix}$

Since the original signal power is

$\begin{matrix}{{\int_{- \infty}^{\infty}{{E\left\lbrack {{{w(t)}{y_{l}(t)}}}^{2} \right\rbrack}\ {t}}} = {\int_{- \infty}^{\infty}{{E\left\lbrack {{{W(f)} \otimes {Y_{l}(f)}}}^{2} \right\rbrack}\ {f}}}} & (71)\end{matrix}$

rejection can be expressed as:

$\begin{matrix}{R^{dB} = {10\log_{10}\frac{\int_{- \infty}^{\infty}{{E\left\lbrack {{{W(f)} \otimes {Y_{l}(f)}}}^{2} \right\rbrack}{f}}}{\int_{- \infty}^{\infty}{{E\left\lbrack {{{{W(f)} \otimes {Y_{l}(f)}} - {Y_{l}(f)}}}^{2} \right\rbrack}{f}}}}} & (72)\end{matrix}$

Y₁(f) can be assumed to be band-limited white Gaussian noise—a justifiedassumption according to the central limit theorem, if the signalx_(l)(t) corresponds to filtered random data samples at 6 MHz, e.g. theDTV signal. This can result in

$\begin{matrix}{{E\left\lbrack {{Y_{l}\left( f_{1} \right)}{Y_{l}^{*}\left( f_{2} \right)}} \right\rbrack} = \left\{ \begin{matrix}{N_{0}{\delta \left( {f_{1} - f_{2}} \right)}} & {f_{1},{f_{2} \in \left\lbrack {{f_{l} - B},{f_{l} + B}} \right\rbrack}} \\0 & {Otherwise}\end{matrix} \right.} & (73)\end{matrix}$

where in some embodiments B=3 MHz. A spectral power of the originalsignal, i.e. E[|W(f){circle around (×)}Y₁(f)|²], can be calculated as:

$\begin{matrix}\begin{matrix}{{E\left\lbrack {{{W(f)} \otimes {Y_{l}(f)}}}^{2} \right\rbrack} = {E\begin{bmatrix}{\int_{- \infty}^{\infty}{{W\left( {f - u} \right)}{Y_{l}(u)}{u}}} \\{\int_{- \infty}^{\infty}{{W^{*}\left( {f - v} \right)}{Y_{l}^{*}(v)}{v}}}\end{bmatrix}}} \\{= {E\begin{bmatrix}{\int_{f_{l} - B}^{f_{l} + B}{{W\left( {f - u} \right)}{Y_{l}(u)}{u}}} \\{\int_{f_{l} - B}^{f_{l} + B}{{W^{*}\left( {f - v} \right)}{Y_{l}^{*}(v)}{v}}}\end{bmatrix}}} \\{= {\int_{f_{l} - B}^{f_{l} + B}{\int_{f_{l} - B}^{f_{l} + B}{{u}{v}\; {W\left( {f - u} \right)}}}}} \\{{{W^{*}\left( {f - v} \right)}{E\left\lbrack {{Y_{l}(u)}{Y_{l}^{*}(v)}} \right\rbrack}}} \\{= {\int_{f_{l} - B}^{f_{l} + B}{\int_{f_{l} - B}^{f_{l} + B}{{u}{v}\; {W\left( {f - u} \right)}}}}} \\{{{W^{*}\left( {f - v} \right)}N_{0}{\delta \left( {u - v} \right)}}} \\{= {N_{0}{\int_{- B}^{+ B}{{{W\left( {f - f_{l} - u} \right)}}^{2}{u}}}}}\end{matrix} & (74)\end{matrix}$

Now considering the spectral power after rejection, i.e. E[|W(f){circlearound (×)}Y₁(f)−Y₁(f)|²]. Inner terms can be expressed:

$\begin{matrix}\begin{matrix}{{{{W(f)} \otimes {Y_{l}(f)}} - {Y_{l}(f)}} = {{{W(f)} \otimes {Y_{l}(f)}} - {\Pi_{2C}\left( {f - f_{l}} \right)}}} \\{\left\lbrack {{W(f)} \otimes {\sum\limits_{k \in \Omega}{Y_{k}(f)}}} \right\rbrack} \\{\approx {{{W(f)} \otimes {Y_{l}(f)}} - {{\Pi_{2C}\left( {f - f_{l}} \right)}\left\lbrack {{W(f)} \otimes {Y_{l}(f)}} \right\rbrack}}} \\{= {\left\lbrack {1 - {\Pi_{2C}\left( {f - f_{l}} \right)}} \right\rbrack {{W(f)} \otimes {Y_{l}(f)}}}}\end{matrix} & (75)\end{matrix}$

where an approximation can be taken because the signal Y₁(f) on channell inside the rectangular window Π_(2C)(f−f_(l)) is far stronger (whichis the reason it is being rejected) than the signals on the otherchannels whose power leakages into the channel are then negligible. Fromthe above, it follows:

$\begin{matrix}\begin{matrix}{{E\left\lbrack {{{{W(f)} \otimes {Y_{l}(f)}} - {Y_{l}(f)}}}^{2} \right\rbrack} = {\left\lbrack {1 - {\Pi_{2C}\left( {f - f_{l}} \right)}} \right\rbrack^{2}{E\left\lbrack {{{W(f)} \otimes {Y_{l}(f)}}}^{2} \right\rbrack}}} \\{{\left\lbrack {1 - {\Pi_{2C}\left( {f - f_{l}} \right)}} \right\rbrack N_{0}}} \\{{\int_{- B}^{+ B}{{{W\left( {f - f_{l} - u} \right)}}^{2}{u}}}}\end{matrix} & (76)\end{matrix}$

Let

K(f)=∫_(−B) ^(+B) |W(f−u)|² du   (77)

The rejection can then be expressed as:

$\begin{matrix}\begin{matrix}{R = \frac{\int_{- \infty}^{\infty}{N_{0}{K\left( {f - f_{l}} \right)}{f}}}{\int_{- \infty}^{\infty}{\left\lbrack {1 - {\Pi_{2C}\left( {f - f_{l}} \right)}} \right\rbrack N_{0}{K\left( {f - f_{l}} \right)}{f}}}} \\{= \frac{\int_{- \infty}^{\infty}{{K(f)}{f}}}{\int_{- \infty}^{\infty}{\left\lbrack {1 - {\Pi_{2C}(f)}} \right\rbrack {K(f)}{f}}}}\end{matrix} & (78)\end{matrix}$

or

$\begin{matrix}{R^{dB} = {10{\log_{10}\left\lbrack \frac{\int_{- \infty}^{\infty}{{K(f)}{f}}}{\int_{- \infty}^{\infty}{\left\lbrack {1 - {\Pi_{2C}(f)}} \right\rbrack {K(f)}{f}}} \right\rbrack}}} & (79)\end{matrix}$

Assuming that the time-domain window is a raised-cosine window:

$\begin{matrix}{{w(t)} = \left\{ \begin{matrix}{\frac{1}{2} + {\frac{1}{2}\cos \left\{ {\frac{\pi}{\beta \; T_{w}}\left\lbrack {t + {\frac{1}{2}\left( {1 - \beta} \right)T_{w}}} \right\rbrack} \right\}}} & {{{- \frac{1}{2}}\left( {1 + \beta} \right)T_{w}} \leq t \leq {{- \frac{1}{2}}\left( {1 - \beta} \right)T_{w}}} \\1 & {{{- \frac{1}{2}}\left( {1 - \beta} \right)T_{w}} \leq t \leq {\frac{1}{2}\left( {1 - \beta} \right)T_{w}}} \\{\frac{1}{2} + {\frac{1}{2}\cos \left\{ {\frac{\pi}{\beta \; T_{w}}\left\lbrack {t - {\frac{1}{2}\left( {t - \beta} \right)T_{w}}} \right\rbrack} \right\}}} & {{\frac{1}{2}\left( {1 - \beta} \right)T_{w}} \leq t \leq {\frac{1}{2}\left( {1 + \beta} \right)T_{w}}} \\0 & {Otherwise}\end{matrix} \right.} & (80)\end{matrix}$

with frequency-domain representation:

$\begin{matrix}{{W(f)} = {\frac{\sin \; \pi \; {fT}_{w}}{\pi \; f}\frac{\cos \left( {{\pi\beta}\; {fT}_{w}} \right)}{1 - {4\beta^{2}f^{2}T_{w}^{2}}}}} & (81)\end{matrix}$

In some embodiments a further assumption can be employed that an FFT ofsize N is employed on input signal samples at 400 MHz such that

$\begin{matrix}{{T_{w}\left( {1 + \beta} \right)} = {\left. {N\; \frac{1}{400}}\Rightarrow T_{w} \right. = \frac{N/400}{\left( {1 + \beta} \right)}}} & (82)\end{matrix}$

where T_(w) is expressed in μs. Note that in some embodiments thesubcarrier spacing (inverse of the FFT period) can be:

$\begin{matrix}{{\frac{400}{N}\mspace{11mu} {MHz}} = {\frac{400 \times 10^{3}}{N}\mspace{11mu} {kHz}}} & (83)\end{matrix}$

Channel Rejection Performance Simulation:

Computer simulation can be employed to compute the rejection expressionof Equation (79).

In some embodiments a 20-30 dB rejection can be sufficient for adouble-ADC architecture as discussed herein. The following table showsthree example configurations that can achieve 20 dB rejection

N β Δ (kHz) 512 0.4 500 1024 0.3 160 2048 0.2 30

Equivalent Discrete-Time Operations for Filtering and Reconstruction:

An embodiment utilizing equivalent discrete-time operations can bedescribed.

A windowing function can be applied

y _(l)(n)=w(n)y(n)   (84)

where w(n) is given by Equation (80) with T_(w) given by Equation (82)and a sampling time t can be replaced by a sampling index

$\begin{matrix}{n = \frac{t}{T_{s}}} & (85)\end{matrix}$

where

$\begin{matrix}{{Y_{1}(k)} = {\frac{1}{\sqrt{N}}{\sum\limits_{n = {{- N}/2}}^{{N/2} - 1}{{y_{1}(n)}^{{- {j2\pi}}\; \frac{k}{N}n}}}}} & (86)\end{matrix}$

is the sampling period.

A FFT can be performed on the resulting signal

$T_{s} = {\frac{1}{400}\mspace{11mu} {µs}}$

A rejection mask Σ_(lεΛ)Π_(2C)(f−f_(i)) can be applied. This operationcan comprise the steps of: finding subcarriers whose indices are in therejection mask; setting Y′(k)=Y₁(k) for those subcarriers; and,nullifying Y′(k) for all other subcarriers.

An inverse Fourier transform can be applied

$\begin{matrix}{{y^{\prime}(n)} = {\frac{1}{\sqrt{N}}{\sum\limits_{k = {{- N}/2}}^{{N/2} - 1}{{Y^{\prime}(k)}^{{j2\pi}\; k\; \frac{n}{N}}}}}} & (87)\end{matrix}$

Signal samples, i.e. y′(n)s, inside the flat portion of the window w(t),i.e. tε[−(1−β)T_(w),(1−β)T_(w)], can be sent to a DAC in order toconstruct a rejection signal y′(t).

In theory, the multiplication of two signals is only equivalent incontinuous-time and discrete-time domains if the output signal isband-limited. Since w(t) is essentially time-limited, it is essentiallynot frequency-limited. However, because in an embodiment w(t) can have abandwidth that is significantly narrower than the sampling bandwidth,i.e. 400 MHz, w(t) can be usefully approximated as a delta function infrequency domain. Under these conditions the continuous- anddiscrete-time multiplications can be essentially equivalent.

A FFT is of finite size can sample the input signal spectrum at onlycertain frequencies. The rejection performance result derived here forthe continuous spectrum can represent an averaged performance.

The operations just described above can construct a rejection signal forthe flat portion of a window. A signal in the nonflat portion of thewindow can require additional compensation that can introduce additionalerror. Constructing a rejection signal for a non-flat portion of awindow can require additional FFT resources. That is, supporting astreaming operation can require overlapping two FFT windows such thattheir flat portions can be connected together.

The graph 2300 of FIG. 23 shows simulated multi-carrier signal powerspectrums at different IP3s (or different Ds). Nonlinearity can causespectrum “shoulders” in adjacent bands. The decibel (dB) differencebetween the inband signal power and the shoulder can be roughly 2D, orthe system dynamic range P_(DR).

The graph 2300 illustrates simulated signal power spectra under varyingdevice nonlinearities in a multi-carrier system with subcarrier spacing100 kHz, β=0.16, number of guard band subcarriers 8 (and number of validdata subcarriers 52). Individual curves 2302 2304 2306 2308 are shownfor IP3-related distance D values of (respectively) 15 dB, 25 dB, 35 dB,and ∞.

In some embodiments with a fixed output power, a higher device IP3 canbe required in order to reduce adjacent channel leakage. In someembodiments, an IP3 requirement can be reduced by applying a digitalpredistortion technique and/or process.

In the foregoing specification, the embodiments have been described withreference to specific elements thereof. It will, however, be evidentthat various modifications and changes may be made thereto withoutdeparting from the broader spirit and scope of the embodiments. Forexample, the reader is to understand that the specific ordering andcombination of process actions shown in the process flow diagramsdescribed herein is merely illustrative, and that using different oradditional process actions, or a different combination or ordering ofprocess actions can be used to enact the embodiments. For example,specific reference to NTSC and/or ATSC and/or DTV embodiments areprovided by way of non-limiting examples. Systems and methods hereindescribed can be applicable to any other known and/or convenientchannel-based communication embodiments; these can comprise singleand/or multiple carriers per channel. The specification and drawingsare, accordingly, to be regarded in an illustrative rather thanrestrictive sense.

1. A system for radio-frequency communications comprising: atransceiver; and, a baseband processor comprising a sensing processorelement, a transmit power control element, wherein the transceiver iscoupled with the baseband processor.